Gaussian Noise

We present DEtection in phase-folded Light curves with cOntrastive Scoring (DELOS), a contrastive-learning-based framework designed to search for shallow transits in Kepler photometry. DELOS combines GPU-accelerated phase folding, optimized phase binning, and a custom one-dimensional convolutional encoder to assign a transit-likeness score to each folded light curve, thereby producing a score periodogram over trial periods without relying on pre-detected threshold-crossing events. Focusing on intermediate-to-long-period signals with orbital periods of 100-150 days, DELOS was trained on 20 million synthetic light curves generated with realistic transit models and Kepler-like noise properties, achieving a validation accuracy of 99.3 percent on the synthetic validation set. In controlled injection-recovery experiments, DELOS improves the combined precision-recall performance by 15.5 percent relative to Box-fitting Least Squares (BLS) and 11.25 percent relative to Transit Least Squares (TLS) in the low Signal-to-Noise Ratios (low-SNR) regime. It also accelerates the search by factors of approximately 3-5 and 74-80 compared with BLS and TLS, respectively. Applied to a selected Kepler validation sample, DELOS recovered all known shallow intermediate-to-long-period transit signals in the tested period range. These results demonstrate that DELOS provides an efficient and sensitive framework for low-SNR transit searches and represents a practical step toward future searches for longer-period terrestrial planets in Kepler, K2, TESS, PLATO, and Earth 2.0 data. Accordingly, this work is intended as a methodological development and validation study, with the detailed astrophysical validation of newly identified candidates deferred to future work.

Error-correcting codes enable reliable communication, yet practical soft decoding remains challenging across code families and block lengths. We propose SB-ECC, a score-based decoder that casts decoding as continuous-time denoising. A neural denoiser defines a probability-flow ordinary differential equation (ODE) that iteratively updates the noisy channel observation toward a valid codeword, guided by parity constraints. The model is trained across noise levels without time/SNR conditioning, enabling inference without SNR estimation and supporting a direct latency accuracy trade off controlled by the ODE solver budget. We use the raw signed channel observation as input for learning a continuous denoising field. Across 42 code/SNR settings, SB-ECC achieves the best BER in 39/42 entries, with an average SNR gain of 0.17dB and a maximum gain of 0.46dB over the strongest competing baseline, we showed that swapping the solver from Euler to DPM preserves -ln(BER) while reducing end-to-end decoding time by 8.86% on average (up to 12.82%).

We design a class of additive noise mechanisms that satisfy $(\varepsilon, δ)$-differential privacy (DP) for scalar, real-valued query functions with known sensitivities, with a particular focus on moderate and low-privacy regimes. These mechanisms, which we call \textit{mixture mechanisms}, are constructed by mixing multiple Gaussian distributions that share the same variance but differ in their means and mixture weights. The resulting distributions can be interpreted as convex combinations of a zero-mean Gaussian (as used in the analytic Gaussian mechanism) and additional Gaussians whose means depend on the sensitivity of the query function. We derive tight conditions on the variances required for $(\varepsilon, δ)$-DP and provide efficient algorithms to compute them. Compared to the analytic Gaussian mechanism, our mechanisms yield substantially lower expected noise amplitudes ($l_1$-loss) and variances ($l_2$-loss for zero-mean distributions). In the low-privacy regime that motivates our design, our mechanisms approach optimality, mitigating nearly all of the optimality gap of the analytic Gaussian mechanism.

As Low Earth Orbit has grown more crowded with space debris, the need for reliable and efficient debris removal solutions becomes more urgent. An active tether-net system with maneuverable units is one of the promising solutions to this problem, whose success is dependent on the robustness of the net maneuver and closing decisions. These in turn are impacted by the uncertainties attributed to i) noisy observation of the target debris state (e.g., sensing errors), and ii) imperfect simulations of the complex net dynamics and net/debris interaction behavior, over which the decision system is trained. This paper focuses on the first of these two uncertainty sources, and presents a pipeline to propagate and quantify the resulting uncertainty in the debris capture performance expressed in terms of Capture Quality Index (CQI). This quantification is uniquely performed for both an active tether-net using a fixed baseline control and one using a trained neuro-control policy to guide the net maneuver during the deployment phase. Two different uncertainty quantification (UQ) techniques, namely Sobol's variance-based sensitivity analysis and perturbation-based method are exploited. A high-fidelity simulator and a lower-fidelity surrogate-based environment are used to demonstrate trade-offs between prediction accuracy versus ease of resolving uncertainties.

We develop semiparametrically efficient inference for kernel measures of noise heterogeneity in additive noise models. In many applications, the regression function is estimated using flexible machine learning methods. Downstream procedures based on the resulting residuals can then inherit first-stage bias: regression error may induce spurious dependence between covariates and residuals, invalidating the assumptions needed for standard analysis. We construct a novel Hilbert-valued one-step estimator of the kernel covariance operator between covariates and residuals. Our estimator yields bootstrap-calibrated tests for residual independence and goodness of fit in additive noise models, while also providing asymptotically efficient confidence intervals for the kernel dependence measure under noise heterogeneity. The framework extends to settings with additional covariates, enabling inference on distributional heterogeneity of residual noise across treatment groups. Simulations show improved calibration and power relative to naive plug-in residual methods.

Recent advances in large language models (LLMs) have facilitated the widespread deployment of LLMs as interactive agents capable of reasoning, planning, and tool use. Despite strong performance on existing benchmarks, such agents often exhibit notable degradation when deployed in real-world settings, where environments are inherently stochastic and imperfect. We argue that this discrepancy arises from a fundamental mismatch between idealized training settings and real-world interaction dynamics, where current paradigms rely on carefully curated task instructions and stable, well-controlled environments. To address this gap, we propose NoisyAgent, an agentic training framework that explicitly incorporates environmental imperfections into the agent learning process. We identify two major sources of interaction noise in real-world scenarios: user noise, which captures ambiguity and variability in user interaction, and tool noise, which reflects failures and anomalies in tool execution. We introduce such perturbations into the training pipeline by modifying user interaction patterns and simulating tool execution results within the training environment. To stabilize training while encouraging agents to handle increasingly challenging imperfections, noise is applied to only a subset of rollouts and progressively increased in difficulty as the model adapts to the current noise level. Extensive experiments demonstrate that our approach consistently improves agent robustness under noisy and dynamic environments. Our analysis reveals that training under noise conditions also yields performance gains on idealized benchmarks, suggesting that controlled exposure to environmental noise promotes more generalizable reasoning and decision-making behaviors. Our findings highlight the importance of modeling interaction imperfections for bridging the gap between agent training and real-world deployment.

Neural networks are known to develop latent representations that are $aligned$, namely structurally similar across networks trained with different architectures, training protocols, or training datasets. We study this phenomenon in a controlled setting, where we train an ensemble of networks on regression and classification tasks using training sets perturbed by independent realizations of a noise process. We show that the signal-to-noise ratio (SNR) and the training sample size influence the alignment in qualitatively similar ways in networks trained on real-world datasets and in an extremely simple $linear$ network with a single hidden layer, for which the alignment can be estimated analytically. Across linear and nonlinear networks, regression and classification tasks, and both synthetic and real-world data, we consistently observe that alignment varies monotonically with SNR but non-monotonically with training sample size. In particular, the alignment is minimized near the interpolation threshold, and a stronger alignment does not necessarily correspond to better generalization error. These findings reveal a non-trivial dependence of alignment on data quality and quantity, decoupled from generalization performance.

Deploying Vision-Language Models on resource-constrained hardware typically requires INT8 quantization, but in joint-embedding architectures such as CLIP this introduces a failure mode distinct from quantized CNN classifiers: activation noise accumulated across transformer blocks perturbs the direction of the multimodal embedding, eroding the cosine alignment on which zero-shot retrieval depends. We characterize this as Quantization-Induced Representation Collapse (QIRC) and quantify it on INT8 CLIP ViT-B/32, where the layer-wise noise-to-signal ratio grows from below 10% in shallow blocks to 52% at Layer 11. We propose LRA-EE (Layer-wise Representation-Aware Early Exit), which bypasses noise-saturated deep layers via Spatio-Semantic Aggregation (replacing the immature shallow [CLS] with a global patch-token average), a learned multi-feature gate (confidence, top-2 margin, spatial-activation variance), and Layer-adaptive Confidence Thresholding calibrated to each layer's Information-to-Noise Ratio. On ImageNet-1K zero-shot classification, LRA-EE reduces FLOPs by 13.4% and improves Top-1 accuracy by +2.44%p (58.72% -> 61.16%) over the INT8 baseline. A four-quadrant decomposition isolates the Rescue Effect: 9.5% of samples are correctly classified at shallow exits but lost to noise at full depth, against only 7.1% suffering the inverse.

We study a nonlinear factor model in which observed responses depend on low-rank latent factors through an unknown monotone link function. This setting is challenging and largely underexplored due to severe nonconvexity and identifiability issues. The link function is assumed to lie in a reproducing kernel Hilbert space (RKHS), enabling flexible nonparametric modeling while preserving identifiability. We formulate the problem as the joint recovery of the low-rank factors, loadings, and the nonlinear link function from possibly incomplete and noisy observations and propose a projected block coordinate descent (BCD) algorithm with explicit regularization to address scale and rotational ambiguities. Under mild incoherence of factors and standard sampling conditions, we establish convergence guarantees in both noiseless and noisy regimes, along with sublinear regret bounds for the link-function updates. Our results extend classical linear factor models to a broad nonlinear regime and provide a principled framework for learning nonlinear latent structures. We evaluate the proposed approach using controlled synthetic experiments, indicating promising performance.

Hybrid post-training usually combines supervised fine-tuning and reinforcement learning, but fixed mixing schedules cannot adapt when the relative noise of the two signals changes over time. We propose GAC, a noise-aware controller that derives an adaptive mixing weight from online estimates of gradient variance and disagreement between the two training signals. The method adds smoothing, prior guidance, and bounded updates while reusing existing training tensors. Experiments on math, code, science, and logic benchmarks show that GAC consistently improves hybrid post-training over strong fixed and rule-based baselines, with larger gains at larger model scales and less than 1% training overhead.

Recently, Deep Image Prior (DIP) has demonstrated strong capabilities for solving inverse imaging problems (IIPs) by optimizing a randomly initialized convolutional neural network in a training-data-free regime. However, DIP suffers from overfitting to noisy measurements due to network over-parameterization, making early stopping (ES) essential. The most successful ES method tracks fluctuations in the running variance of the network output to detect overfitting. However, in many applications, these fluctuations may appear prematurely, leading to unstable reconstructions. In this paper, we first show that nearly optimal DIP early stopping can be achieved when two independent noisy copies of the degraded image are available. Motivated by this observation, and since obtaining two fully independent copies is infeasible, we propose an overfitting detection framework based on constructing pseudo self-referenced images, resulting in three IIP-specific algorithms. Our approach is further supported by theoretical results on single-reference validation, pseudo-validation estimation, and the impact of shared noise. Across different IIPs, ranging from natural image restoration to medical image reconstruction, and under varying noise levels and noise types, our methods consistently outperform existing DIP early stopping approaches, all without requiring an accurate estimate of the noise level.

Large Language Models (LLMs) have been widely adopted in conversational applications. However, their reliance on parametric knowledge limits reliability in real-world scenarios that require dynamic or domain-specific information. Retrieval-Augmented Generation (RAG) addresses this limitation by incorporating external knowledge during generation, but existing text-based and graph-based RAG methods often struggle with noisy or irrelevant contexts. In this work, we propose Structure-aware Retrieval Augmented Generation (SA-RAG), which uses tables as an intermediate structured representation to provide a compact and controllable interface that reduces noise while preserving essential information. We introduce a quality-aware table metadata generation framework that models metadata normalization and effectiveness, improving metadata quality and downstream performance. Furthermore, we explore both training-free and training-based table generation methods. Generation validation and direct preference optimization further improve table quality while maintaining semantic and structural consistency. Experiments on two noisy real-world datasets show that SA-RAG significantly outperforms existing RAG baselines. Our code is publicly available at a public repository.

In this note, I would like to share a small research moment where Codex helped me find the right way to adapt rare switching to the private setting. The standard determinant-based update rule in linear bandits and RL works beautifully because the design matrix grows monotonically. But once Gaussian noise is added for privacy, this monotonicity can fail, and the usual analysis no longer goes through. The key reason is that determinant growth controls volume, while regret analysis needs control of the worst direction. To address this, Codex comes up with a different rare-switching rule based on the generalized Rayleigh quotient, which restores logarithmic policy updates and the desired confidence-width comparison up to a constant factor. I present my manually clean-up version of the proof here as well as some personal reflection on this example.

Real-world time-series data in industrial sensing, healthcare, and energy systems is often corrupted by a mixture of Gaussian noise and occasional large-magnitude impulse outliers. For tasks that depend on local shape, such as ECG morphology analysis and battery degradation monitoring, the main requirement is not only low reconstruction error but also preservation of derivative peaks and task-critical features. We propose Cascade-KDE, a training-free restoration framework for corrupted time series. The method first estimates a two-dimensional temporal-amplitude density, then applies a Density-Truncated Robust Expectation to limit the influence of distant abnormal points, and finally refines the sequence through an exponential cascade with adaptive stopping. This design aims to improve robustness under out-of-distribution impulse corruptions while keeping the restored trajectory close to the original local structure. Across several benchmark datasets, the proposed method shows consistent gains over classical filters and representative learning-based baselines on curve fidelity, derivative preservation, downstream classification, and runtime efficiency. These results suggest that bounded density-based restoration is a practical option for feature-preserving preprocessing in noisy time-series pipelines.

Frozen Vision Foundation Models (VFMs) with lightweight classification heads are increasingly used in medical imaging because they offer efficient and reproducible deployment. Yet noisy-label learning methods for this frozen-feature regime remain poorly understood, and most existing methods still rely on a small-loss assumption inherited from end-to-end training. We present a controlled benchmark of eight noisy-label methods across five medical datasets, three backbones, two noise types, and five noise rates (150 conditions, 6,000 training runs), evaluated with balanced accuracy. The benchmark shows that there is no universal winner: Friedman ranking over the 150 conditions yields $χ^2 = 333.2$ ($p = 4.77 \times 10^{-68}$), ELR wins the most conditions (49/150), while CUFIT attains the best mean rank (2.51). The practical cost of method choice grows sharply with noise severity, from 4.5pp on clean data to 18.8pp at asymmetric 40% noise. To explain these benchmark-level patterns, we revisit the small-loss assumption in a representative high-risk regime. Under frozen DINOv2 features, clean and noisy loss distributions overlap by 53--61%, and matched-rate clean-sample detection shows that prediction agreement is markedly more stable than loss ranking under asymmetric noise (3pp vs.\ 13pp precision drop). On ISIC2019 with asymmetric 40% noise, Co-Teaching reaches 68% overall accuracy while collapsing to 35.1% balanced accuracy with zero recall on three minority classes. Together, these results recast noisy-label learning for frozen VFMs as a regime-aware method-selection problem rather than a search for a single dominant algorithm. We conclude with evidence-based guidance and a low-regret feature-space selector for practical recommendation.

Kernel methods are typically formulated under the assumption of exact, noise-free access to the Gram matrix. However, in emerging settings such as quantum machine learning, each kernel entry must be inferred from noisy observations, and its accuracy depends on how a limited measurement budget is allocated. Despite this, existing approaches overwhelmingly rely on uniform allocation, which equalizes estimator variance but ignores the highly non-uniform dependence of kernelized classifiers on the Gram matrix. In this work, we introduce an adaptive measurement-allocation strategy for learning kernelized Support Vector Machines (SVMs) from noisy Bernoulli observations. Our approach combines two complementary principles: (i) geometric sensitivity, capturing how perturbations of individual kernel entries affect the classifier margin, and (ii) active-set instability, quantifying the probability of discrete changes in support-vector membership induced by measurement noise. These signals define a task-aware allocation scheme that concentrates measurements on the most decision-critical regions of the kernel matrix. We provide a theoretical analysis showing that the benefit of adaptive allocation is governed by the heterogeneity of the induced kernel importance structure, leading to distinct regimes in which adaptive or uniform strategies are preferable. Empirical evaluations on synthetic datasets demonstrate that adaptive allocation significantly improves support-vector recovery, margin estimation, and decision-function accuracy under fixed measurement budgets. A dual-coefficient stability criterion further enables early stopping, achieving near-optimal performance while using only a fraction of the measurement cost. Additional experiments on quantum kernels derived from real-world data reveal a regime-dependent behavior aligned with known phenomena such as kernel concentration. Together...

We investigate unpaired image inverse problems, a challenging setting where only independent, non-paired sets of noisy measurements and clean target signals are available for training. We propose a novel inverse problem solver based on Unbalanced Optimal Transport, called Unbalanced Optimal Transport Map for Inverse Problems (UOTIP). Our method formulates the reconstruction task, predicting clean target signals from noisy measurements, as learning a UOT Map from noisy measurement distribution to clean signal distribution by incorporating a likelihood-based cost function. By relaxing the exact marginal constraint, the UOT framework provides key advantages to our model: robustness to multi-level observation noise, adaptability to class imbalance between noisy and clean datasets, and generalizability to diverse noise-type scenarios. Furthermore, we theoretically demonstrate that incorporating a quadratic cost term ensures the existence and uniqueness of the transport map by satisfying the twist condition, even for ill-posed inverse problems. Our experiments demonstrate that UOTIP achieves state-of-the-art performance on unpaired image inverse problem benchmarks, across linear and nonlinear inverse problems.

Hyperparameter prediction is a critical practical bottleneck for model-based image denoisers, ranging from classical TV/TGV variational solvers to modern diffusion-based models such as DiffPIR. While existing learned predictors can achieve near-oracle performance, this approach scales poorly: each new configuration conventionally requires its own oracle-labeled training set, and each label requires a hierarchical grid search evaluated against clean ground truth. We therefore ask whether oracle supervision collected on source configurations can transfer to target configurations with few or no target oracle labels. We propose HyperDn, a single configuration-conditioned predictor that pools oracle supervision across source configurations and predicts heterogeneous hyperparameters for new denoiser--noise configurations. In a cross-paradigm experiment, HyperDn transfers from relatively cheap TV/TGV variational sources to more expensive diffusion-based DiffPIR. With only $2$ target oracle labels, it reaches $30.23$,dB, within $0.90$,dB of the oracle, and outperforms the $64$-label per-configuration predictor trained from scratch, using $1/32$ as many target labels as that baseline point. Without any target oracle labels, HyperDn also reaches near-oracle PSNR on two unseen mixtures of seen noise types and on transfer from relatively cheap $96\times 96$ source images to $512\times 768$ targets. Together, these results show that expensive oracle supervision for hyperparameter prediction can be transferred from source to new target configurations, reducing the need to rebuild oracle labels for each new denoising configuration.

Channel foundation models assume access to fully observed channels, an assumption that fails in deployment. We introduce PilotWiMAE, a self-supervised framework whose encoder ingests noisy pilot observations directly and whose attention factorizes along the axis separating temporal from joint space-frequency processing, an inductive bias inspired by the physics of the problem. Pilot input shrinks the observation space by up to two orders of magnitude and also removes the unrealistic assumption of full-CSI availability while incurring lower latency. The factorized design generates robust representations by exploiting the separable channel structure and allows a pretraining mask ratio of $99\%$. We pair patch-normalized reconstruction, which captures small-scale fading structure, with an auxiliary scale loss that recovers the large-scale fading features, and use an AWGN curriculum to match pilot noise at pretraining and deployment. Pretrained solely on $3.5$,GHz and evaluated at $28$,GHz across in-distribution and out-of-distribution settings, PilotWiMAE's cross-frequency beam selection and channel characterization beat supervised baselines despite operating on a smaller observation space. To weaken the coupling between decoder capacity and representation quality, we further propose a decoder-centric pretraining stage following the encoder-decoder joint pretraining, which allows PilotWiMAE to demonstrate competitive channel estimation without sacrificing representation quality. To foster further work in this direction, we release the PilotWiMAE pretrained weights and training pipeline, together with CSIGen, our Sionna-based ray-tracing channel-generation tool, and the channel datasets used in this work.

Noise-tolerant PAC learning of linear models has been of central interests in machine learning community since the last century. In recent years, many computationally-efficient algorithms have been proposed for the problem of learning linear threshold functions under multiple noise models. Yet, when the problem is considered under multiclass learning settings, i.e. when the number of classes $k$ is at least $3$, it is unknown whether there exist computationally-efficient PAC learning algorithms when the data sets are maliciously corrupted. In this paper, we consider that the marginal distribution is a mixture of bounded variance distributions and the data sets satisfy a margin condition at the same time. We show that there exists a computationally-efficient algorithm that PAC learns multiclass linear classifiers $\{h_w:x\mapsto \arg\max_{y\in[k]}w_y\cdot x, x\in \mathbb{R}^d, w\in\mathbb{R}^{kd}\}$ using at most $O(k^2\cdot (d\log d+\log k))$ samples even under a constant rate of nasty noise. Our algorithm consists of two main ingredients: a cluster-based pruning scheme and a standard multiclass hinge loss minimization program. Even in the special case of binary setting, i.e. $k=2$, our result is strictly stronger than all prior works.

A lightweight and reproducible denoising pipeline for high-throughput Raman spectroscopy is presented. The approach relies on a one-dimensional convolutional autoencoder trained using a Noise2Noise strategy, requiring neither external spectral libraries nor high signal-to-noise reference spectra for training. From a reduced training subset composed of repeated short-exposure acquisitions, the model learns to reconstruct Raman spectra while efficiently suppressing stochastic noise. The method is evaluated on a heterogeneous mineral sample, using both quantitative spectral fidelity metrics (RMSE, SNR, SSIM) and task-oriented criteria based on unsupervised K-means classification. Results demonstrate that integration times as short as 5 ms per spectrum, which are typically insufficient for reliable interpretation, yield denoised spectra with high fidelity to the reference data while preserving chemically coherent maps. This work provides a practical trade-off between spectral quality and acquisition speed, enabling fast, adaptable Raman workflows compatible with routine laboratory use. It also offers a transferable framework for other one-dimensional spectroscopic modalities.

Generative models can produce nonsensical text, unrealistic images, and unstable materials faster than simulation or human review can absorb; without per-sample confidence, trust erodes. Existing fixes run $k$ ensembles or stochastic trajectories at $k\times$ compute, measuring variability between models, not model confidence. We propose Flow Matching with Confidence (FMwC). FMwC injects input-dependent multiplicative noise at selected layers, propagates its variance through the network in closed form, and integrates it along the ODE trajectory, yielding a per-sample confidence score at standard sampling cost. The score supports multiple uses: filtering improves image quality and thermodynamic stability of crystals; editing rewinds trajectories to the points where the model commits and redirects them; and adaptive stepping concentrates ODE compute where the flow is ambiguous. We find that the confidence score correlates with the magnitude of the divergence of the learned velocity field, which gives us a window to understand the generative process, opening up surgical forms of guidance that target the moments that matter, new sampling algorithms and interpretability of generative models.

Our preliminary experiments on gym-DSSAT maize irrigation tasks revealed that +/-2 degrees C temperature noise causes an 11.9% reduction in economic returns for PPO policies trained under clean conditions - a systematic robustness deficit that existing research has not adequately addressed. This paper tackles three interconnected limitations impeding practical deployment of agricultural RL systems: the trade-off between early-stage learning efficiency and late-stage generalization capability; the naive additive combination of intrinsic and extrinsic rewards in exploration-augmented PPO; and uniform measurement noise injection strategies that disregard empirically validated differential sensitivity across agricultural state variables. We introduce three systematic innovations: Progressive Generalization Augmentation (PGA) implementing a three-phase curriculum (clean training 0-800 episodes, progressive 800-1200, full augmentation 1200-2000); a deeply coupled RND-PPO architecture with dual-channel GAE normalization, progress-decayed intrinsic coefficients, and semantic discretization; and domain-prioritized noise injection with hierarchical activation. Our experimental evaluation demonstrates: 8.43% yield improvement and 16.42% nitrogen use efficiency improvement over SOTA BERT-DQN in Florida; 5.61% yield improvement in Zaragoza (though 3.67% lower economic score due to challenging Mediterranean climate); and 94.4% vs 80.0% performance retention under combined perturbations. All experiments used 5 random seeds on NVIDIA A100 GPUs with 4.2+/-0.3 hours per run (2000 episodes, 2048-step buffer, 64 mini-batch size).

While Local Differential Privacy (LDP) serves as a foundational primitive for distributed data collection, its stringent randomization requirements often lead to severe degradation in data representation utility. This degradation stems from the task-agnostic nature of conventional LDP mechanisms, which perturb all dimensions without accounting for their relative importance to the downstream objective. To address this issue, we propose a novel approach that mitigates noise in task-relevant subspaces of the data representation. Our method identifies task-critical subspaces via the Jacobian of a public downstream model, selectively attenuates noise along these directions, and reshapes the isotropic noise of standard LDP mechanisms into an anisotropic distribution. The resulting mechanism preserves the privacy guarantee of the underlying LDP randomizer while heterogeneously modulating the impact of noise across task directions, thereby substantially enhancing data utility. The approach is applicable to both linear and nonlinear models and can be seamlessly integrated with existing LDP mechanisms. Extensive experiments on CIFAR-10-C under brightness corruption at the highest severity level demonstrate that integrating our approach improves classification accuracy by approximately 8 percentage points for Laplace and 20 percentage points for PrivUnit variants at $ε=7.5$. The source code is available at https://github.com/ymha/jacobian-anr-ldp.

High-resolution remote sensing imagery is critical for environmental monitoring, urban mapping, and land cover analysis, but its transmission is often hindered by limited bandwidth and high communication costs. Conventional pipelines transmit full-resolution pixel data, resulting in redundant and inefficient delivery. This paper proposes a text-guided remote sensing image transmission system that replaces complete high-resolution data with low-resolution images accompanied by compact textual descriptions. An onboard text generator produces spatial and semantic summaries, reducing the transmitted data volume to approximately 2% of the original size. For ground-based reconstruction, a text-conditioned image restoration model is introduced, which leverages cross-modal learning to recover fine spatial details and maintain semantic coherence. Experimental results on the Alsat-2B, UC Merced Land Use, and Aerial Image datasets demonstrate that the proposed framework achieves reconstruction PSNRs of 16.36 dB, 26.87 dB, and 27.41 dB, respectively, enabling efficient and information-preserving image transfer for remote sensing applications. The implementation will be made publicly available at \href{https://github.com/haoyangofficial/textrssr}{GitHub}.

Deep neural networks are vulnerable to adversarial perturbations, limiting deployment in safety-critical applications such as synthetic aperture radar (SAR) automatic target recognition (ATR). Randomized smoothing improves robustness by averaging predictions over noisy inputs, but isotropic noise often fails to preserve the semantic structure of SAR imagery. We propose semantic smoothing, a defense that replaces noised-based perturbations with structured randomized transformations generated by a novel view synthesis model. For SAR, we condition on acquisition geometry to synthesize multiple plausible radar views. Predictions across generated randomized views are aggregated to form a robust classifier. Experiments show that semantic smoothing improves robustness against standard attacks, such as FGSM and PGD, and SAR-specific attacks, such as OTSA and SMGAA, while also increasing clean classification accuracy. These results demonstrate that randomized smoothing via semantically preserving geometric transformations is a promising alternative to isotropic noise for adversarial defense in structured sensing domains.

We study nonconvex stochastic optimization under the Blum-Gladyshev ($\mathsf{BG}$-0) noise model, where the stochastic gradient variance grows quadratically with the distance from the initialization. We consider this problem under both standard smoothness and the symmetric generalized-smoothness framework, which captures objectives whose local curvature can scale with the gradient norm. We prove that normalized stochastic gradient descent with momentum, using only one stochastic gradient per iteration, converges under $\mathsf{BG}$-0 noise with oracle complexity $O(\varepsilon^{-6})$. This rate holds both for standard smoothness and for $α$-symmetric generalized smoothness, showing that generalized smoothness is rate-neutral for normalized momentum in this setting. We then study a variance-reduced normalized STORM method. Under mean-square smoothness and sharp initialization, the method achieves the minimax optimal $O(\varepsilon^{-4})$ complexity, matching the lower bound. Under expected $α$-symmetric generalized smoothness, the STORM recursion couples gradient-dependent smoothness with distance-dependent noise, leading to complexity $O(\varepsilon^{-(4+α)})$ for $α\in(0,1)$ and $O(\varepsilon^{-5})$ for $α=1$. When the distance-growth parameter in the noise model vanishes, our guarantees recover the standard bounded-variance rates: $O(\varepsilon^{-4})$ for momentum, $O(\varepsilon^{-3})$ for variance reduction, and $O(\varepsilon^{-2})$ in the deterministic case. To our knowledge, these are the first convergence guarantees for normalized methods in non-convex stochastic optimization under $\mathsf{BG}$-0 noise without bounded domains, increasing batch sizes, or explicit anchoring, covering both standard and generalized smoothness regimes.

Irregularly sampled multivariate event streams remain a difficult modality for generative modeling: tokenization-based approaches break down when inter-event intervals vary by orders of magnitude. We (i) propose \textbf{SurF}, a generative model that uses the Time Rescaling Theorem (TRT) as a learnable bijection between event sequences and i.i.d.\ unit-rate exponential noise, enabling a single model to be trained across heterogeneous event-stream datasets; (ii) three efficient parameterizations of the cumulative intensity that scale to long sequences; and (iii) a Transformer-based encoder for multi-dataset pretraining. On six real-world benchmarks, SurF achieves the best reported time RMSE on Earthquake, Retweet, and Taobao, and is within trial-level noise of the strongest specialist on the remaining three. Under a strict leave-one-out protocol, the held-out checkpoint beats every classical and neural-autoregressive baseline on $5/6$ datasets and beats every baseline on Amazon and Earthquake, an initial step toward foundation models over asynchronous event streams (Code is available at https://github.com/MrRezaeiUofT/SurF).

Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity. This motivation is intuitive: if the data are heavy-tailed, HT noise may appear better matched than light-tailed (LT) Gaussian noise. However, replacing Gaussian noise by HT noise also changes the underlying estimation problem. In this paper, we revisit this paradigm through a combined theoretical and empirical study, establishing sampling-error bounds for two representative diffusion models driven by HT and LT noise. We show that HT noise makes the statistical estimation problem harder, leading to less favorable sampling-error bounds. We support these findings with experiments on synthetic and real-world datasets, empirically recovering the predicted error trade-off. Our results call into question a growing design trend in generative modeling and challenge the use of HT noise to improve rare-region exploration.

Continuous diffusion is a natural framework for non-autoregressive generation but has generally lagged behind masked discrete diffusion models (MDMs) on discrete sequence generation. We argue that the bottleneck is not continuity itself, but a representation in which denoising depends on timestep-indexed noise regimes. We introduce \emph{Discrete Stochastic Localization} (DSL), a continuous-state framework with unit-sphere token embeddings whose Bayes-optimal denoiser is invariant to the nominal signal-to-noise ratio (SNR) under the localization channel. One trained network then supports an entire family of per-token SNR paths, with endpoint masked-diffusion paths as a special case. Fine-tuning a pretrained MDLM checkpoint with DSL substantially improves distributional faithfulness (MAUVE) on OpenWebText across all step budgets from $T{=}128$ to $T{=}1024$, and the same checkpoint supports random-order autoregressive sampling, as well as a hybrid continuous-then-discrete sampler using as few as T=48 total steps -- without distillation or retraining.

In large-scale visual recognition and data mining tasks, the presence of noisy labels severely undermines the generalization capability of deep neural networks (DNNs). Prevalent sample selection methods rely primarily on training loss or prediction confidence for passive screening. However, within a feature space degraded by noise, decision boundaries undergo systematic boundary collapse. This phenomenon hinders the ability of the model to distinguish between hard clean samples and noisy samples at the decision margins, thereby creating a significant performance bottleneck. This study is the first to emphasize the pivotal importance of active boundary restoration for noise-robust learning. We propose HamBR, a novel paradigm based on Hamiltonian dynamics. The core approach leverages the Spherical Hamiltonian Monte Carlo (Spherical HMC) mechanism to actively probe inter-class ambiguous regions within the representation space and synthesize high-quality virtual outliers. By imposing explicit repulsion constraints via energy-based modeling, these synthesized samples establish robust energy barriers at the decision boundaries. This mechanism forces real samples to move from dispersed overlapping regions toward their respective class centers, thereby restoring the discriminative sharpness of the decision boundaries. HamBR demonstrates exceptional versatility and can be integrated as a plug-and-play defense module into existing semi-supervised noisy label learning frameworks. Empirical evaluations show that the proposed paradigm significantly enhances the discriminative accuracy of hard boundary samples, achieving state-of-the-art (SOTA) performance on CIFAR-10/100 and real-world noise benchmarks. Furthermore, it exhibits superior convergence efficiency and reliable robustness, while improving significantly the capability of the model for Out-of-Distribution (OOD) detection.

Optical readout in low-light imaging is fundamentally limited by measurement noise, including photon shot noise, detector noise, and quantization error. In this regime, downstream inference depends not only on the optical front end, but also on how noisy high-dimensional sensor measurements are represented before classification or decision-making. Here we show that eigentasks provide a measurement-adapted representation for optical sensor outputs by ordering readout features according to their resolvability under noise. Using experimental data from a lens-based optical imaging system and a reanalysis of published data from a single-photon-detection neural network, we find that eigentask representations frequently outperform standard baselines including principal component analysis and filtering-based compression. The advantage is most pronounced in photon-limited, few-shot, and higher-difficulty classification regimes. In few-shot MPEG-7 classification, for example, the advantage over other methods reaches about 10 percentage points as the number of classes increases. In these settings, eigentasks yield more informative low-dimensional features and improve sample-efficient downstream learning. These results identify measurement-adapted representation as a promising strategy for optical inference when photon budget, acquisition time, and task complexity are constrained.

Despite rapid progress in Vision-Language-Action (VLA) models for robotic control, instruction drift remains a persistent failure mode in long-horizon tasks. This paper reconceptualizes this phenomenon, positing that instruction drift is fundamentally a systematic sampling error: local greedy sampling is prone to collapsing into "Negative Pivotal Windows"--irreversible local optima with high local probability that sever global success pathways. To address this, we propose Context-Aware Power Sampling (CAPS), a training-free inference-time computation framework. CAPS leverages power distributions to sharpen global trajectory probabilities, enabling lookahead search over the model's conditional generative trajectory distribution. Furthermore, we introduce a metacognitive control mechanism based on Signal-to-Noise Ratio (SNR). This mechanism triggers adaptive MCMC search solely when drift risk is detected, enabling a dynamic transition from "intuitive fast thinking" to "rational slow search." Experiments on RoboTwin, Simpler-WindowX, and Libero-long benchmarks show that CAPS achieves substantial improvements over strong baselines, including OpenVLA and TACO, without parameter updates. These results support the effectiveness of adaptive inference-time computation for improving long-horizon robustness in embodied control.

This paper relaxes the restrictive symmetry conditions adopted in [4], [5] and extends their universal feature selection framework to accommodate noisy observations as well as attribute structures that may exhibit directional preferences. We introduce the notion of weak spherical symmetry, quantified by second-moment distances, which allows controlled deviations from rotational invariance. Under this relaxed condition, we develop a universal feature selection framework based on the singular value decomposition of the canonical dependence matrix computed from noisy data. Our main result shows that the selected features achieve asymptotically optimal error exponents up to a residual term that depends on the symmetry deviation $δ$ and the noise levels $η_1, η_2$. When $δ, η_1, η_2$ are relatively small, our result recovers that of [5], thereby demonstrating that exact spherical symmetry is unnecessary. Overall, our findings highlight the robustness of the selection framework against second-moment deviations and observation noise, thereby broadening its applicability across diverse inference tasks and providing a theoretically grounded tool for universal feature selection in practical scenarios.

Poisson subsampling is the default sampling scheme in differentially private machine learning, largely because its unstructured randomness yields tractable privacy amplification analyses. Yet this same randomness introduces substantial participation variance: each sample appears in very different numbers of training iterations. In this work, we show that this variance is not merely a practical artifact to be tolerated, but a fundamental source of suboptimal privacy amplification. We prove that Balanced Iteration Subsampling (BIS), a structured scheme in which each sample participates in exactly a fixed number of iterations, achieves stronger privacy amplification than Poisson subsampling and is optimal at both extremes of the noise spectrum ($σ\to 0$ and $σ\to \infty$). Our analysis reveals that the privacy-noise tradeoff is governed not by maximizing randomness, but by eliminating participation variance while preserving uniform marginal participation across iterations. To translate this asymptotic theory into finite-noise guarantees, we introduce a practical near-exact Monte Carlo accountant for BIS, which removes the analytical slack of existing RDP and composition-based PLD analyses. Evaluations across more than 60 practical DP-SGD configurations show that BIS consistently outperforms Poisson subsampling in the low-noise regimes most relevant for high-utility private training, reducing the required noise multiplier by up to $9.6\%$. These results overturn the common intuition that more sampling randomness necessarily yields stronger privacy amplification: in DP-SGD, structured participation can be both more practical and more private. Our implementation is available at https://github.com/dong-xin-ao-andy/bis-mc-accountant.

Denoising wearable electroencephalogram (EEG) is inherently challenging since neural activity is not only subtle but also inseparable from spectrally overlapping noise artifacts. Classical signal processing methods, relying on fixed or heuristic rules, cannot handle the time-varying pervasive artifacts in wearable EEGs. Deep learning methods, on the other hand, show promise in decomposition-free EEG denoising using highly expressive neural networks, but the training requires artifact-free EEG, which is inherently unobtainable. To address this, we propose Intelligent Partitioning for Self-supervised Denoising (iPSD). Our method eliminates the need for clean references by learning to partition an input EEG segment into independent noisy realizations with the same underlying signal. This enables self-supervision of deep learning denoisers, even in zero-shot settings where only a single EEG segment to be denoised is available. We validate iPSD through extensive experiments, including validations on wearable EEG from in-ear sensors. The results show that iPSD achieves state-of-the-art performance, most notably under extremely low signal-to-noise ratios (down to -10 dB) and challenging artifacts (e.g., EMG), with spectral fidelity orders of magnitude higher than competitive baselines.

High-resolution rainfall observations are crucial for weather forecasting, water management, and hazard mitigation. Traditional operational measurements are often biased and low-resolution, limiting their ability to capture local rainfall. Accurate high-resolution rainfall maps require integrating sparse surface observations, yet existing deep learning densification methods are hindered by rainfall's skewed, localized nature, noise, and limited spatio-temporal fusion. We present DropsToGrid, a Neural Process-based method that generates dense rainfall fields by fusing temporal sequences from noisy, irregularly distributed private weather stations with spatial context from radar. Leveraging multi-scale feature extraction, temporal attention, and multi-modal fusion, the model produces stochastic, continuous rainfall estimates and explicitly quantifies uncertainty. Evaluations on real-world datasets demonstrate that DropsToGrid outperforms both operational and deep learning baselines, generating accurate high-resolution rainfall maps with well-calibrated uncertainty, even when only few stations are available and in cross-regional scenarios.

The impressive performance of large language models (LLMs) arises from their massive scale and heterogeneous module composition. However, this structural heterogeneity introduces additional optimization challenges. While adaptive optimizers such as Adam(W) provide per-parameter adaptivity, they do not explicitly account for module-level gradient heterogeneity, resulting in slower convergence, suboptimal performance, or training instability. Existing approaches typically rely on manually tuned module-specific learning rates or specific optimization strategies, which are computationally costly and difficult to generalize across tasks or models. To establish a more principled approach, we first analyze the noise-damping behavior of Adam in high-noise modules and introduce \textbf{Module-wise Learning Rate Scaling via SNR (MoLS)}. MoLS estimates module-level SNRs to scale Adam updates, allowing automated module-wise learning rate allocation without manual tuning. Empirical results through multiple LLM training benchmarks demonstrate that MoLS improves convergence speed and generalization, achieving performance comparable to carefully tuned module-specific learning rates, while remaining compatible with memory-efficient training algorithms.

While Separate Source-Channel Coding (SSCC) retains the practical benefits of modular system design, its effectiveness in noisy text transmission is fundamentally constrained by the fragility of autoregressive source decoding. In low-SNR regimes, even a small number of residual bit errors after channel decoding may derail the subsequent lossless reconstruction process, especially when Arithmetic Coding (AC) relies on Large Language Model (LLM)-based probability estimation. Existing remedies either strengthen channel decoding based solely on channel observations or introduce contextual information only at the receiver for post-hoc correction, yet neither fully addresses the fragility of source probability modeling under residual channel errors. To this end, this paper proposes a Memory-Augmented Source Coding (MASC) scheme for robust SSCC-based transmission. Rather than treating context as external side information, MASC internalizes contextual patterns into a source model shared by both the transmitter-side source encoder and the receiver-side source decoder. Specifically, MASC employs a shared Parameterized Contextual Memory (PCM) to encode multi-order $n$-gram patterns, and further introduces a Mixture-of-Memory-Experts Router (MMER) to perform sparse, hidden-state-dependent routing over memory experts during autoregressive source modeling. By adaptively activating only the most relevant memories at each coding step, MASC refines source probability estimation, shortens average codelength, and mitigates the sensitivity of source decoding to residual channel errors. Extensive experiments over Rayleigh fading and AWGN channels demonstrate the effectiveness of the proposed scheme compared with state-of-the-art methods.

Causal reasoning in natural language requires identifying relevant variables, understanding their interactions, and reasoning about effects and interventions, often under noisy or ambiguous conditions. While large language models (LLMs) exhibit strong general reasoning abilities, they struggle to disentangle correlation from causation, particularly when observations are partially incorrect or irrelevant information is present. In this work, we introduce NoisyCausal, a new benchmark designed to evaluate causal reasoning under structured noise. Each instance is generated from a ground-truth causal graph and contextualized with a natural language scenario by injecting controllable forms of noise, such as irrelevant distractors, value perturbations, confounding, and partial observability. Moreover, we propose a modular reasoning framework that combines LLMs with explicit causal structure to address these challenges. Our method prompts the LLM to extract variables, construct a causal graph from context, and then reformulates the reasoning task as a structured prompt grounded in this graph. Rather than relying on statistical patterns alone, the LLM is guided by symbolic structure, enabling more interpretable and robust inference. Experimental results show that our method significantly outperforms standard prompting and reasoning baselines on NoisyCausal. Furthermore, it generalizes well to external benchmarks such as Cladder without task-specific tuning. Our findings highlight the importance of combining causal abstractions with language-driven reasoning to achieve faithful and robust causal understanding in LLMs.

Accurate, unified models for event cameras (ECs) remain elusive, hampering calibration and algorithm design. We develop a foundational probabilistic model for EC event detection, grounded in photon statistics, that unifies the description of static scene noise events and step response curves (S-curves) within a single analytical framework. Three formulations of the probability distributions are derived, spanning all intensity regimes: exact Poisson, saddle-point, and Gaussian. The model reveals the underlying connection between these otherwise disparate EC behaviors and clarifies the interpretation of S-curves, which we show is more nuanced than selecting a fixed probability threshold. Based on this model, we propose Noise2Params, a method for determining camera-specific values of the log-contrast threshold $B$, the lux-to-photon conversion factor $α$, and the leakage term $θ$ (found to be intensity dependent), via error minimization against observed noise-event distributions. Noise2Params requires only recordings of static, uniform scenes, offering an experimentally accessible alternative to approaches that demand specialized dynamic light sources. We further support the validity the model by training convolutional neural networks (CNNs) on synthetic noise images generated from our distributions and evaluating their ability to reconstruct static scenes from experimental data. We further demonstrate the utility of our model by showing that CNNs incorporating synthetic data outperform those trained solely on experimental data. Our framework provides a quantitative foundation for EC calibration, noise-aware algorithm design, and applications in photon-limited regimes.

We study the problem of black-box optimization of a function f of any dimension, given function evaluations perturbed by noise. The function is assumed to be locally smooth around one of its global optima, but this smoothness is unknown. Our contribution is an adaptive optimization algorithm, POO or parallel optimistic optimization, that is able to deal with this setting. POO performs almost as well as the best known algorithms requiring the knowledge of the smoothness. Furthermore, POO works for a larger class of functions than what was previously considered, especially for functions that are difficult to optimize, in a very precise sense. We provide a finite-time analysis of POO's performance, which shows that its error after n evaluations is at most a factor of sqrt(ln n) away from the error of the best known optimization algorithms using the knowledge of the smoothness.

The nonuniform and growing impact of adversarial noise across the layers of deep neural networks has been used in the literature, without a formal mathematical justification, to detect adversarial inputs and improve robustness. In this work, we study this phenomenon in detail and present a formal adversarial noise amplification theorem. We specify a set of sufficient conditions under which the adversarial noise amplification is mathematically guaranteed. Based on theoretical observations, we propose a novel training methodology with a custom spectral loss function and a specific architectural design to enhance the amplification signal for detecting adversarial data. Finally, we introduce a new, lightweight detection mechanism that leverages the enhanced amplification signal and operates entirely at inference time. To validate our approach, we demonstrate the detector's efficacy against both state-of-the-art attacks and a purpose-built adaptive attack, confirming that enhanced amplification can serve as a robust and reliable signal for adversarial defense.

Unlearnable examples (UEs) aim to compromise model training by injecting imperceptible perturbations to clean samples. However, existing UE schemes exhibit limited robustness against advanced defenses due to their heuristic design or narrowly scoped domain perturbations. To address this, we propose \texttt{DUNE}, a \underline{\textbf{D}}ual-branch \underline{\textbf{UN}}learnable \underline{\textbf{E}}nsemble perturbation optimization approach. Specifically, \texttt{DUNE} separately optimizes perturbations in the spatial and color domains to establish the mapping between perturbations and shift-induced labels. This design extends the perturbation domain to increase noise intensity for improving robustness and drives the models to learn perturbation-oriented features with degraded generalization, thereby achieving unlearnability. To strengthen \texttt{DUNE}'s performance, we further propose an unlearnability-enhancing ensemble strategy that aggregates diverse pre-trained models during the dual-branch optimization. Extensive experiments on benchmark datasets CIFAR-10 and ImageNet verify that \texttt{DUNE}'s robustness outperforms 12 SOTA UE schemes under 7 mainstream defenses, yielding a lower average test accuracy of 14.95% to 50.82%.

We introduce Hybrid Convolutions with Attention Stochasticity (HyCAS), an adversarial defense that narrows the long-standing gap between provable robustness under L2 certificates and empirical robustness against strong L attacks, while preserving strong generalization across diverse imaging benchmarks. HyCAS unifies deterministic and randomized principles by coupling 1-Lipschitz, spectrally normalized convolutions with two stochastic components, spectral normalized random, projection filters and a randomized attention-noise mechanism, to realize a randomized defense. Injecting smoothing randomness inside the architecture yields an overall <= 2-Lipschitz network with formal certificates. Exten-sive experiments on diverse imaging benchmarks, including CIFAR-10/100, ImageNet-1k, NIH Chest X-ray, HAM10000, show that HyCAS surpasses prior leading certified and empirical defenses, boosting certified accuracy by up to 7.3% (on NIH Chest X-ray) and empirical robustness by up to 3.1% (on HAM10000), without sacrificing clean accuracy. These results show that a randomized Lipschitz constrained architecture can simultaneously improve both certified L2 and empirical L adversarial robustness, thereby supporting safer deployment of deep models in high-stakes applications. Code: https://github.com/misti1203/HyCAS

Perception for automated driving is largely based on onboard environmental sensors, such as cameras and radar, which are cost-effective but limited by line-of-sight and field-of-view constraints. These inherent limitations may cause onboard perception to fail under occlusions or poor visibility conditions. In parallel, cooperative awareness via vehicle-to-everything (V2X) communication is becoming increasingly available, enabling vehicles and infrastructure to share their own state as object-level information that complements onboard perception. In this work, we study how such V2X information can be integrated into 3D object detection and how robust the resulting system is to realistic V2X imperfections. Using the nuScenes dataset, we emulate object-level cooperative awareness messages from ground truth, injecting controlled noise and object dropout to mimic real-world conditions such as latency, localization errors, and low V2X penetration rates. We convert these messages into a dedicated bird's-eye view (BEV) input and fuse them into a BEVFusion-style detector. Our results demonstrate that while object-level cooperative information can substantially improve detection performance, achieving an NDS of 0.80 under favorable conditions, models trained on idealized data become fragile and over-reliant on V2X. Conversely, our proposed noise-aware training strategy, coupled with explicit confidence encoding, enhances robustness, maintaining performance gains even under severe noise and reduced V2X penetration.

The demand for high-resolution subsurface imaging and continuous Earth monitoring has driven rapid growth in active and passive seismic data from dense geophone deployments, distributed acoustic sensing (DAS) arrays, and large-scale 2D and 3D surveys. This expansion makes complex noise suppression increasingly challenging, especially when signal fidelity must be preserved. Conventional supervised deep learning methods are often task-specific, require large paired datasets, and can suffer from domain shift under new acquisition conditions. Foundation models offer a promising alternative, but pre-training seismic foundation models from scratch requires massive domain-specific data and substantial computation. We propose an efficient framework that repurposes general-purpose Vision Foundation Models (VFMs) for geophysical tasks through Parameter-Efficient Fine-Tuning. The architecture uses a pre-trained VFM, a DINOv3 encoder, adapted with Low-Rank Adaptation (LoRA) to enable effective feature adaptation with few additional parameters. To improve robustness under unseen field conditions without ground truth, we introduce a kurtosis-guided unsupervised test-time adaptation module that updates only LoRA parameters during inference. This module self-calibrates the model to site-specific noise by identifying information-rich regions via kurtosis and performing self-training without labeled data. Experiments on public exploration seismic images and DAS vertical seismic profiling data from the Utah FORGE site show that the framework matches or outperforms domain-specific models. Tests on unseen cross-site data from a land survey in China and the Groß Schönebeck geothermal site in Germany further demonstrate strong generalization and effective signal-noise separation. These results highlight the potential of adapting pre-trained VFMs to data-intensive problems in exploration seismology.

Joint image compression and wireless transmission remain relatively underexplored compared to generic image restoration, despite its importance in practical communication systems. We formulate this problem under an equivalent linear model, and propose Diffusion-OAMP, a training-free reconstruction framework that embeds a pre-trained diffusion model into the OAMP algorithm. In Diffusion-OAMP, the OAMP linear estimator produces pseudo-AWGN observations, while the diffusion model serves as a nonlinear estimator under an SNR-matching rule. This framework offers a way to incorporate multiple generative priors into OAMP. Experiments with varying compression ratios and noise levels show that Diffusion-OAMP performs favorably against classic methods in the evaluated settings.

Motivated by sensing modalities in modern autonomous systems that involve hardware-constrained spatial sampling over large arrays with limited coherence time, we develop a novel framework for rapid super-resolution multi-signal direction-of-arrival (DoA) estimation based on Hankel-structured sensing and data matrix decomposition of arbitrary rank, under both the $L_2$ and $L_1$-norm formulation. The resulting $L_2$-norm estimator is shown to be maximum-likelihood optimal in white Gaussian noise. The $L_1$-norm estimator is shown to be maximum-likelihood optimal in independent, identically distributed (i.i.d.) isotropic Laplace noise, offering broad robustness to impulsive interference and corrupted measurements commonly encountered in practice. Extensive simulations demonstrate that the proposed methods exhibit powerful super-resolution capabilities, requiring significantly lower SNR and achieving substantially higher resolution probability than recent competing approaches.

Compositional text-to-image (T2I) generation requires a model to honour multiple sub-prompts that describe distinct image regions. Recent work shows that the \emph{starting noise} of a diffusion model carries significant semantic information: ``golden'' noise predicted from text can substantially raise prompt fidelity. We observe that this noise prediction is, however, fundamentally global: the same network is asked to summarise a long, multi-region prompt with a single text embedding, which becomes the bottleneck whenever the prompt describes scenes with spatially-separated entities. We introduce \textbf{Golden RPG}, a region-aware noise predictor that extends a frozen NPNet with two trainable additions: (i) a per-region \textbf{FiLM adapter} that reshapes the predicted noise according to each sub-prompt; and (ii) a \textbf{Region Cross-Attention} layer injected between two stages of the Swin backbone, allowing different spatial locations to attend to different sub-prompt tokens. To prevent the regional conditioning from degrading samples whose prompts are already easy, we further propose a \textbf{Confidence-Adaptive Blending} head that dynamically predicts, per sample, how strongly the regional signal should override the global signal. We evaluate on the original RPG benchmark (20 prompts, 100 samples) and on four multi-region categories of T2I-CompBench (1{,}200 images, six competing methods). Golden RPG achieves the highest Cross-Region-Coherence score on every category, while matching the strongest baselines on absolute CLIP-Score and CLIP-IQA. A paired user study further shows a $\boldsymbol{\sim}$67% preference over the strongest baseline. The adapter contains $\sim$2M trainable parameters and adds only $0.6$,s of inference overhead on top of SDXL.

With the evolution of 6G, semantic communication has emerged as a promising paradigm by prioritizing the delivery of task-relevant meaning over strict bit-level correctness. However, existing transport mechanisms still rely on explicit port headers and bit-level validation, making them vulnerable to header corruption and the resulting packet loss. To address this issue, this paper proposes a Semantic Port-Aware Adaptive-Rate Transmission Protocol (SPAT) for semantic communication. The proposed framework jointly embeds source and destination port information into semantic representations, thereby reducing dependence on explicit port headers while enabling robust port-aware transmission. Furthermore, a differentiated semantic processing mechanism is developed for uplink and downlink scenarios, where port identification is introduced for uplink service recognition and destination-aware conditional gating is designed for downlink selective decoding. In addition, an adaptive-rate controller is incorporated to dynamically adjust the number of transmitted semantic channels according to channel conditions and feature importance, thereby improving both robustness and transmission efficiency. Experimental results on the AFHQ and ImageNet-10 datasets, together with real-world experimental measurements, demonstrate that SPAT consistently outperforms TCP, UDP, and SITP in reconstruction quality across different SNRs while maintaining low-latency transmission.

Randomized Smoothing (RS) offers formal $\ell_2$ guarantees for arbitrary base classifiers but faces two key practical bottlenecks: (i) it often relies on noise-augmented training to achieve nontrivial certificates, which increases training cost, can reduce clean accuracy, and weakens RS as a genuinely post-hoc defense; and (ii) certification is computationally expensive, typically requiring tens of thousands of noisy forward passes per input, which hinders deployment, especially on resource-constrained edge devices. To address both limitations, we propose Laplace-Bridged Smoothing (LBS), an analytic reformulation of RS that replaces high-dimensional input-space Monte Carlo (MC) sampling with efficient computations in a low-dimensional probability space. LBS preserves formal robustness guarantees without requiring noise-augmented training while substantially reducing certification burden. On CIFAR-10 and ImageNet, LBS attains stronger certified robustness than RS and reduces per-sample certification cost by nearly an order of magnitude. Notably, on NVIDIA Jetson Orin Nano and Raspberry Pi 4, LBS achieves speedups of up to $494\times$, enabling practical certified deployment on real-world edge devices. Finally, we provide theoretical justification for the analytic formulation and certificate validity of LBS.

We propose Noise-Based Spectral Embedding (NBSE), a physics-informed framework for selecting informative features from high-dimensional data without greedy search. NBSE constructs a sparse similarity graph on the samples and identifies the Nishimori temperature $β_N$ the critical inverse temperature at which the Bethe Hessian becomes singular. The corresponding smallest eigenvector captures the dominant mode of an intrinsically degree-corrected diffusion process, naturally reweighting nodes to prevent hub dominance. By transposing the data matrix and applying NBSE in feature space, we obtain a one-dimensional spectral embedding that reveals groups of redundant or semantically related dimensions; balanced binning then selects one representative per group. We prove that coloured Gaussian perturbations shift $β_N$ by at most $O(\barσ^2)$, guaranteeing robustness to measurement noise. Experiments on ImageNet embeddings from MobileNetV2 and EfficientNet-B4 show that NBSE preserves classification accuracy even under aggressive compression: on EfficientNet-B4 the accuracy drop is below $1\%$ when retaining only $30\%$ of features, outperforming ANOVA $F$-test and random selection by up to $6.8\%$.

Accurately estimating friction coefficients between arbitrary material pairs is critical for robotics, digital fabrication, and physics-based simulation, but exhaustive pairwise testing scales quadratically with the number of materials. We introduce a proxy-based modeling framework that approximates any pairwise friction $f(A,B)$ from a small, fixed set of proxy materials $C=[c_1,\dots,c_k]$ by learning a per-material embedding $z_A = g(f(A,c1),\dots,f(A,ck))$ and a fusion function $p$ such that $f(A,B)\approx p\big(z_A,z_B\big)$. We present deterministic and probabilistic realizations of $g$ and $p$, procedures for selecting diverse proxy sets, and mechanisms for handling missing or noisy proxy measurements. The learned embeddings are compact, interpretable, and enable calibrated uncertainty estimates for downstream decision making. On simulated and measured friction datasets, our approach achieves high predictive accuracy, robust performance with partial observations, and substantial experimental savings by significantly reducing pairwise testing.

Fine-tuned autoregressive models for graph-to-sequence generation (G2S) often struggle with factual grounding and edit sensitivity. To tackle these issues, we propose a non-autoregressive diffusion framework that generates text by iterative refinement conditioned on an input graph, named as Diffusion Language Model for Graphs (DLM4G). By aligning graph components (entities/relations) with their corresponding sequence tokens, DLM4G employs an adaptive noising strategy. The proposed strategy uses per-token denoising error as a signal to adaptively modulate noise on entity and relation tokens, improving preservation of graph structure and enabling localized updates under graph edits. Evaluated on three datasets, DLM4G consistently outperforms competitive G2S diffusion baselines trained on identical splits across both surface-form and embedding-based metrics. DLM4G further exceeds fine-tuned autoregressive baselines up to 12x larger (e.g., T5-Large) and is competitive with zero-shot LLM transfer baselines up to 127x larger. Relative to the strongest fine-tuned PLM baseline, DLM4G improves factual grounding (FGT@0.5) by +5.16% and edit sensitivity (ESR) by +7.9%; compared to the best diffusion baseline, it yields gains of +3.75% in FGT@0.5 and +23.6% in ESR. We additionally demonstrate applicability beyond textual graphs through experiments on molecule captioning, indicating the method's generality for scientific G2S generation.

Noisy labels are a pervasive challenge in medical image classification, where annotation errors arise from inter-observer variability and diagnostic ambiguity. Although several noise-robust learning methods have been proposed, their evaluation predominantly relies on accuracy-oriented metrics, overlooking the clinical implications of asymmetric error costs. In medical diagnosis, a false negative (missed disease) carries substantially higher consequences than a false positive (false alarm), as delayed treatment can directly impact patient outcomes. In this work, we investigate whether noise-robust training methods preserve clinical safety under label noise. We conduct a systematic risk-aware evaluation of the state-of-the-art noise-robust methods Coteaching, DivideMix, UNICON, and a GMM-based filtering approach on binarized DermaMNIST and PathMNIST datasets under clean and label noise rates of 20%, and 40%. Beyond balanced accuracy, we adopt a cost-sensitive Global Risk formulation that explicitly penalizes false negatives. Our analysis reveals that the robustness of state-of-the-art methods does not guarantee clinical safety. Furthermore, we demonstrate that integrating cost-sensitive optimization into noise-robust training significantly reduces clinical risk, while mantaining model utility. These findings demonstrate that noise-robust learning must be evaluated through a clinical risk lens, and that combining robust training with cost-sensitive optimization can meaningfully reduce risk in noisy-label medical imaging scenarios.

Text-to-image diffusion models have achieved remarkable generative capabilities, yet accurately aligning complex textual prompts with synthesized layouts remains an ongoing challenge. In these models, the initial Gaussian noise acts as a critical structural seed dictating the macroscopic layout. Recent online optimization and search methods attempt to refine this noise to enhance text-image alignment. However, relying on unconstrained Euclidean gradient ascent mathematically inflates the latent norm and destroys the standard Gaussian prior, causing severe visual artifacts like color over-saturation. Furthermore, these methods suffer from inefficient semantic routing and easily fall into the ``reward hacking'' trap of external proxy models. To address these intertwined bottlenecks, we propose Oracle Noise, a zero-shot framework reframing noise initialization as semantic-driven optimization strictly confined to a Riemannian hypersphere. Instead of relying on complex external parsers, we directly identify the most impactful structural words in the prompt to efficiently route optimization energy. By updating the noise strictly along a spherical path, we mathematically preserve the original Gaussian distribution. This geometric constraint eliminates norm inflation and unlocks aggressive step sizes for rapid convergence. Extensive experiments demonstrate that Oracle Noise significantly accelerates semantic alignment and achieves superior aesthetics without black-box models. It completely mitigates Euclidean-induced degradation, establishing state-of-the-art performance across human preference metrics (e.g., HPSv2, ImageReward), semantic alignment (CLIP Score), and sample diversity, all within a strict 2-second optimization budget.

Solutions to the Schrödinger bridge problem and its generalizations yield feedback control policies for optimal density steering over a controlled diffusion. To numerically compute the same, the dynamic Sinkhorn recursion has become a standard approach. The mathematical engine behind this approach is the Hopf-Cole transform that recasts the conditions for optimality into a system of boundary-coupled linear PDEs. Recent works pointed out that for the control-affine Schrödinger bridge problem, this exact linearity via Hopf-Cole transform, and thus the standard Sinkhorn recursion, apply only if the control and noise channels are proportional. When the channels do not match, the Hopf-Cole-transformed PDEs remain nonlinear, and no algorithm is available to solve the same. We advance the state-of-the-art by designing a Sinkhorn recursion with memory that leverages the structure of these nonlinear PDEs, and demonstrate how it solves the control-affine Schrödinger bridge problem with input and noise channel mismatch. We prove the local stability of the proposed algorithm.

Segmentation is central to clinical diagnosis and monitoring, yet the reliability of modern foundation models in medical imaging still depends on the availability of precise prompts. The Segment Anything Model (SAM) offers powerful zero-shot capabilities, although it collapses under the weak, generic, and noisy prompts that dominate real clinical workflows. In practice, annotations such as centerline points are coarse and ambiguous, often drifting across neighboring anatomy and misguiding SAM toward inconsistent or incomplete masks. We introduce SPD, a Saliency-Guided Prompt Distillation framework that converts these unreliable cues into robust guidance. SPD first learns data-driven anatomical priors through a lightweight saliency head to obtain confident localization maps. These priors then drive Contextual Prompt Distillation, which validates and enriches noisy prompts using cues from anatomically adjacent slices, producing a consensus prompt set that matches the behavior of expert reasoning. A Pairwise Slice Consistency objective further enforces local anatomical coherence during segmentation. Experiments on four challenging MRI and CT benchmarks demonstrate that SPD consistently outperforms existing SAM adaptations and supervised baselines, delivering large gains in both region-based and boundary-based metrics. SPD provides a practical and principled path toward reliable foundation model deployment in clinical environments where only imperfect prompts are available.

Federated learning (FL) enables training of a global model while keeping raw data on end-devices. Despite this, FL has shown to leak private user information and thus in practice, it is often coupled with methods such as differential privacy (DP) and secure vector sum to provide formal privacy guarantees to its participants. In realistic cross-device deployments, the data are highly heterogeneous, so vanilla federated learning converges slowly and generalizes poorly. Clustered federated learning (CFL) mitigates this by segregating users into clusters, leading to lower intra-cluster data heterogeneity. Nevertheless, coupling CFL with DP remains challenging: the injected DP noise makes individual client updates excessively noisy, and the server is unable to initialize cluster centroids with the less noisy aggregated updates. To address this challenge, we propose PINA, a two-stage framework that first lets each client fine-tune a lightweight low-rank adaptation (LoRA) adapter and privately share a compressed sketch of the update. The server leverages these sketches to construct robust cluster centroids. In the second stage, PINA introduces a normality-driven aggregation mechanism that improves convergence and robustness. Our method retains the benefits of clustered FL while providing formal privacy guarantees against an untrusted server. Extensive evaluations show that our proposed method outperforms state-of-the-art DP-FL algorithms by an average of 2.9% in accuracy for privacy budgets (epsilon in {2, 8}).